11/15/99

1. When I was young and impressionable, my dad told me that Voltaire had said, "If you would speak with me, first define your terms." Although I have been unable to confirm this quote, I was able to find a similar sentiment expressed by Tryon Edwards. He said "A large part of the discussions of disputants come from the want of accurate definition.--Let one define his terms and then stick to the definition, and half the differences in philosophy and theology would come to an end, and be seen to have no real foundation."

2. In the years after hearing my dad's advice, I noticed (just by listening, as Yogi Berra might have said) that most disagreement stems from a lack of understanding of the other point of view, which is usually caused by the people having different definitions for the same terms.

3. Still later, when I studied mathematics, I learned about rigor. Rigor means that mathematics demands that in the development of the theory, strict and precise rules be followed. One of these rules is that before using a term, it must first be specifically defined. Mathematicians acknowledge no truth about what a term means, and in fact, you are at liberty to define any term any way you like. Rigor, however, demands that you remain consistent in your definition and use of each term throughout your discussion.

4. Although it probably wouldn't be advisable to be this rigorous in ordinary conversation, it still wouldn't hurt to move a little in that direction, especially when we are trying to learn something by discussing a serious topic with someone.

5. Thinking about the unsuitability for rigor in ordinary conversation reminds me of a comedy tape a friend of mine played for me. There were a couple of British comedians of the Monty Python variety having a conversation. One guy is holding up two or three apples and grinning gleefully as he answered the questions from the other guy: "Do you have an apple?" "No." . . . "Do you have some apples?" "No.". . . "Do you have apples?" "Yes."

6. You had to be there and hear it to get the humor, but this example shows you how extreme rigor would confound normal discussions.

7. But if you are in a serious discussion trying to discern the truth, then I think a rigorous definition of terms pays off. In fact, in a Socratic dialog, I think the most useful question you can contribute is "What, exactly, did you mean by that?" This question can be thrown into a dialog at almost any point, and in addition to giving you some time to reflect on the discussion without having to commit yourself to a position, it can actually help clear things up.

8. Just as in mathematics, I think we should feel free to adopt any definition for any term in any discussion.

9. This is not usually done, or even condoned. People commonly take the position that there is a 'correct' definition for terms and if you don't use them in that way, you are in error. I guess I would have to say that in most ordinary conversations, this is a good position to take because in ordinary conversations, people don't take the time to define terms, and if the standard definitions aren't used, it causes a lot of confusion. So for ordinary conversation, I am not recommending any change.

10. A Socratic dialog, or any serious discussion attempting to get at the 'truth', is a different matter and I think this is a very useful, if not necessary, posture to take.

11. Mentioning 'truth' brings up another tenet of mathematical rigor. In mathematics, no notion of truth outside the context of the discussion is acknowledged. A mathematical proposition is said to be 'true' or 'false' based on the rules of logic and the specific definitions of terms in a particular discussion, but nothing is said about any absolute truth or even any concept of truth that goes beyond the context of the discussion.

12. I'm usually not much for poetry, but I do like this poem by Clarence R. Wylie, Jr.

PARADOX
Not truth, nor certainty. These I foreswore
In my novitiate, as young men called
To holy orders must abjure the world.
'If . . . , then . . . ,' this only I assert;
And my successes are but pretty chains
Linking twin doubts, for it is vain to ask
If what I postulate be justified,
Or what I prove possess the stamp of fact.

Yet bridges stand, and men no longer crawl
In two dimensions. And such triumphs stem
In no small measure from the power this game,
Played with the thrice-attenuated shades
Of things, has over their originals.
How frail the wand, but how profound the spell!

13. As a result of this position, mathematicians have no qualms or hesitation in discussing propositions that may be utterly false in fact. If in our religious, or political, or other sensitive discussions we could feel this same freedom, I think it would disarm a lot of hostility and allow us to get on with the business of understanding each others thoughts, modifying our own thoughts, and articulating our thoughts to others. This is how progress can be made in a serious discussion.

14. So, to sum up, I think that at least this much mathematical rigor should be adopted for all serious discussions of philosophy or religion: We should define all terms that are likely to be misunderstood. We should feel free to define the terms in any way we think will help others to understand. We should stick to these definitions in each and every use of the defined terms. And we should feel free to discuss any proposition in spite of whether some people consider it to be false or not.